From a user perspective, does it make sense to have a different recursion_limit per interpreter? I don't see a problem with it. However, does it make sense to also keep a global value that we default to when a per-interpreter value is not set? I think it might.
I suppose a bigger question is what users will expect the recursion limit (AKA "sys.getrecursionlimit()") to be for a newly created subinterpreter. Will it be some global default? Will it be the value from the parent interpreter? I'd go with a global default, which would imply that the default value should be stored under _PyRuntimeState like we had it (but still keep the actual per-interpreter field for the actual value).
FWIW, the existing docs don't really block either approach.